On large angle multiple gluon radiation

TL;DR

The paper analyzes jet-shape observables in e+e- annihilation with phase-space restrictions, showing that a two-variable associated distribution factorizes: the global V-distribution and a non-global SL distribution in E_out evaluated at the scaled energy VQ. It develops a Mellin-based resummation framework distinguishing a global radiator from a non-global radiator, deriving explicit Sudakov and two-gluon correlation contributions, and demonstrates all-orders factorization in the large-Nc limit via a non-linear evolution (BMS-type) equation. The work provides analytic control over non-global logarithms by relating the E_out dependence to hedgehog configurations and shows asymptotic behavior where the non-global piece grows as Δ^2 with a universal angular structure, with geometry-dependent corrections computable numerically. This contributes a practical method to predict and mitigate non-global effects in jet-shape measurements, with extensions to other observables like broadening.

Abstract

Jet shape observables which involve measurements restricted to a part of phase space are sensitive to multiplication of soft gluon with large relative angles and give rise to specific single logarithmically enhanced (SL) terms (non-global logs). We consider associated distributions in two variables which combine measurement of a jet shape V in the whole phase space (global) and that of the transverse energy flow away from the jet direction, Eout (non-global). We show that associated distributions factorize into the global distribution in V and a factor that takes into account SL contributions from multi-gluon ``hedgehog'' configurations in all orders. The latter is the same that describes the single-variable Eout distribution, but evaluated at a rescaled energy VQ.